The rate of change of surface area of a sphere of radius $r$ when the radius is increasing at the rate of 2 cm/sec is proportional to

$r$

Let S be the surface area and $r$ be the radius of the sphere at any time t. Then,

$S=4 \pi r^2$

$\Rightarrow \frac{d S}{d t}=8 \pi r \frac{d r}{d t}$

$\Rightarrow \frac{d S}{d t}=8 \pi r \times 2$             [$\frac{d r}{d t}$ = 2 cm/sec]

$\Rightarrow \frac{d S}{d t}=16 \pi r \Rightarrow \frac{d S}{d t} \propto r$